Determine all integers n≥1 for which there exists n real numbers x1,…,xn in the closed interval [−4,2] such that the following three conditions are fulfilled:
- the sum of these real numbers is at least n.
- the sum of their squares is at most 4n.
- the sum of their fourth powers is at least 34n.
(Proposed by Gerhard Woeginger, Austria) inequalitiesalgebrasystem of equationsalgebra unsolved